Step by step
The question
Question: find x.
The two triangles are similar: sides 6, 8, 9 and 12, 16, x.
1 Match the sides
Similar means the same shape.
One triangle is a bigger copy of the other.
Matching sides go together: the shortest with the shortest, the longest with the longest.
Here both lists go in the same order.
The first sides go together: 6 and 12.
The second sides: 8 and 16.
The third sides: 9 and x.
2 Find the scale factor
The scale factor k says how many times bigger.
We use a pair we know both of: 12 and 6.
k is big over small.
Careful!
The big side goes on top: 12/6, not 6/12.
12 divided by 6 is 2.
Every side of the big triangle is 2 times its partner.
3 Find x
x is in the big triangle.
Its partner in the small one is 9.
So x is 9 times 2.
That is 18.
So x = 18.
4 Check
Let's check with the other pair: 8 times 2 should be 16.
And x with its partner: 18/9 is 2 too.
Every pair has the factor 2.
So x = 18 is right!
Let's look back.
First: match the sides.
Then: find the scale factor.
Then: find x.
Last: check.